The Exceedance Design Effect: Effective Sample Size for Thresholds under Clustering
Suppose we want a cutoff that 90% of a population falls below. We estimate it from a sample, and another sample would give a different cutoff and a different fraction below it. We ask how much that fraction varies when observations come in independent groups, such as pupils in classrooms or sentences in news articles. We prove that grouping multiplies its large-sample variance by $1+(m-1)ρ_I(p)$, where $m$ is the group size, $p$ is the target fraction, and $ρ_I(p)$ measures whether two members of a group fall on the same side of the cutoff. That correlation can differ from the correlation between the scores themselves, and it changes with the target. We give a direct proof, a counterexamp...
| Authors | Adam Noonan |
|---|---|
| Primary category | stat.ML |
| Published | 21 August 2026 |
| Last updated at source | 1 October 2026 |
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